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Modelling Conditional Dependence Between Response Time and Accuracy

Author

Listed:
  • Maria Bolsinova

    (Utrecht University
    CITO, Dutch National Institute for Educational Measurement
    University of Amsterdam)

  • Paul Boeck

    (Ohio State University
    KU Leuven)

  • Jesper Tijmstra

    (Tilburg University)

Abstract

The assumption of conditional independence between response time and accuracy given speed and ability is commonly made in response time modelling. However, this assumption might be violated in some cases, meaning that the relationship between the response time and the response accuracy of the same item cannot be fully explained by the correlation between the overall speed and ability. We propose to explicitly model the residual dependence between time and accuracy by incorporating the effects of the residual response time on the intercept and the slope parameter of the IRT model for response accuracy. We present an empirical example of a violation of conditional independence from a low-stakes educational test and show that our new model reveals interesting phenomena about the dependence of the item properties on whether the response is relatively fast or slow. For more difficult items responding slowly is associated with a higher probability of a correct response, whereas for the easier items responding slower is associated with a lower probability of a correct response. Moreover, for many of the items slower responses were less informative for the ability because their discrimination parameters decrease with residual response time.

Suggested Citation

  • Maria Bolsinova & Paul Boeck & Jesper Tijmstra, 2017. "Modelling Conditional Dependence Between Response Time and Accuracy," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1126-1148, December.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:4:d:10.1007_s11336-016-9537-6
    DOI: 10.1007/s11336-016-9537-6
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    References listed on IDEAS

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    Cited by:

    1. Inhan Kang & Minjeong Jeon & Ivailo Partchev, 2023. "A Latent Space Diffusion Item Response Theory Model to Explore Conditional Dependence between Responses and Response Times," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 830-864, September.
    2. Jinxin Guo & Xin Xu & Zhiliang Ying & Susu Zhang, 2022. "Modeling Not-Reached Items in Timed Tests: A Response Time Censoring Approach," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 835-867, September.
    3. Th'eo Durandard & Matteo Camboni, 2024. "Comparative Statics for Optimal Stopping Problems in Nonstationary Environments," Papers 2402.06999, arXiv.org, revised Jul 2024.
    4. Inhan Kang & Paul Boeck & Roger Ratcliff, 2022. "Modeling Conditional Dependence of Response Accuracy and Response Time with the Diffusion Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 725-748, June.
    5. Minjeong Jeon & Paul Boeck & Xiangrui Li & Zhong-Lin Lu, 2020. "Trivariate Theory of Mind Data Analysis with a Conditional Joint Modeling Approach," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 398-436, June.
    6. Kang, Inhan & De Boeck, Paul & Partchev, Ivailo, 2022. "A randomness perspective on intelligence processes," Intelligence, Elsevier, vol. 91(C).
    7. Fang Liu & Xiaojing Wang & Roeland Hancock & Ming-Hui Chen, 2022. "Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1290-1317, December.
    8. Maria Bolsinova & Jesper Tijmstra, 2019. "Modeling Differences Between Response Times of Correct and Incorrect Responses," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1018-1046, December.
    9. Zhaojun Li & Paul De Boeck & Jian Li, 2020. "Does planning help for execution? The complex relationship between planning and execution," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-17, August.
    10. Inhan Kang & Dylan Molenaar & Roger Ratcliff, 2023. "A Modeling Framework to Examine Psychological Processes Underlying Ordinal Responses and Response Times of Psychometric Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 940-974, September.
    11. Sun-Joo Cho & Sarah Brown-Schmidt & Paul De Boeck & Matthew Naveiras & Si On Yoon & Aaron Benjamin, 2023. "Incorporating Functional Response Time Effects into a Signal Detection Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 1056-1086, September.
    12. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    13. Meredith Langi & Minjeong Jeon, 2023. "Identifying and Supporting Academically Low-Performing Schools in a Developing Country: An Application of a Specialized Multilevel IRT Model to PISA-D Assessment Data," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 332-356, March.
    14. Minjeong Jeon & Paul Boeck & Jevan Luo & Xiangrui Li & Zhong-Lin Lu, 2021. "Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 239-271, March.

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